In this page arithmetic series we are going to see ,how to find the sum of n terms in an arithmetic series.The formula,meaning of each term in that formula and also example problems with detailed steps.

The method used to find the sum of an A.P is known by Gaussian method of addition,named after German mathematician.Karl Friedrich Gauss(1777-1855 A.D). He found two formulas to find the sum of n terms to an Arithmetic progression.

Sequence

1. Sequence is nothing but set of numbers.

2. Each number is separated by commas.

Series

1.Series is nothing but sum of terms.

2. Each number is separated by positive sign.

Now let us see the formula to find sum of n terms.

sn = n⁄2 [2a + (n-1)d]

sn = n⁄2 [a + l]

Here a = First term

d = Common difference

n = number of terms

l = last term

Both are the formulas to find the sum of n terms.The first formula will be used if the last term is not given. However the last term is given we need to the second formula.

Some times if we are not given the number of terms in the series. We can find the number of terms by using the following formula.

n = (l-a)⁄d + 1

Example 1:

Find the sum of the series 1 + 3 + 5 + .............+ 399

Solution:

Here we need to find the sum of the series 1 + 3 + 5 + .............+ 399

We don't know how many terms are in the series.So we have to use the formula to find how many terms are in the series.

The first term (a) = 1

Common difference (d) = 3-1

= 2

and the last term (l) = 399

n =[ (399-1) / 2 ] + 1

n = ( 398/2 ) + 1

= 199 + 1

n = 200

We have 200 terms in the arithmetic series.Here we have last term.So we can use the second formula.

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